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A373250 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j) and i mod A181819(i) = j mod A181819(j), for all i, j >= 1, where A181819 is the prime shadow of n.

%I A373250 #7 May 30 2024 18:48:21
%S A373250 1,2,3,4,3,5,3,6,7,5,3,8,3,5,9,10,3,8,3,11,12,5,3,13,4,5,14,15,3,16,3,
%T A373250 17,12,5,9,18,3,5,9,19,3,20,3,11,21,5,3,22,4,11,9,15,3,13,9,23,12,5,3,
%U A373250 24,3,5,21,25,12,20,3,11,12,16,3,26,3,5,21,15,12,16,3,27,28,5,3,24,12,5,9,29,3,30,9,11,12,5,9,31,3,11,21
%N A373250 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j) and i mod A181819(i) = j mod A181819(j), for all i, j >= 1, where A181819 is the prime shadow of n.
%C A373250 Restricted growth sequence transform of the ordered pair [A181819(n), A373247(n)].
%C A373250 For all i, j:
%C A373250   A373251(i) = A373251(j) => a(i) = a(j),
%C A373250   a(i) = a(j) => A101296(i) = A101296(j),
%C A373250   a(i) = a(j) => A373246(i) = A373246(j),
%C A373250   a(i) = a(j) => A373249(i) = A373249(j),
%C A373250   a(i) = a(j) => A353566(i) = A353566(j).
%H A373250 Antti Karttunen, <a href="/A373250/b373250.txt">Table of n, a(n) for n = 1..100000</a>
%o A373250 (PARI)
%o A373250 up_to = 100000;
%o A373250 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A373250 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A373250 Aux373250(n) = [A181819(n), n%A181819(n)];
%o A373250 v373250 = rgs_transform(vector(up_to, n, Aux373250(n)));
%o A373250 A373250(n) = v373250[n];
%Y A373250 Cf. A101296, A181819, A353566, A373246, A373247, A373249, A373251.
%K A373250 nonn
%O A373250 1,2
%A A373250 _Antti Karttunen_, May 30 2024